X-ray systems, particularly CT systems with quantum-counting detectors, and methods for evaluating the detector pulses originating from the detectors are generally known. More recently, as distinct from the previously used conventional detector types with integrating detector elements, quantum-counting detectors of the type in question have been proposed for use in CT systems because they offer a possible solution to the problem of reducing the patient dose and of energy-resolving measurement in single-source CT systems. In the case of such quantum-counting detectors, the high X-ray photon fluxes lead, in clinical CT scanners, to the build-up of space charges in the CdTe/CdZnTe detector—materials that are typically used, which can result in significant count rate drift. This count rate drift makes precise dose determination more difficult and leads, in general, to imaging errors and, particularly severely in CT systems, to artifacts in the tomographic images created from absorption data.